O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

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Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter. The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated. In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations. In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm. The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two). Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.

In this thesis, we deal with finite Gibbs point processes, especially the processes with densities with respect to a Poisson point process. The main aim of this work is to investigate a four-parametric marked point process of circular discs in three dimensions with two and three way point interactions. In the second chapter, our goal is to simulate such a process. For that purpose, the birth- death Metropolis-Hastings algorithm is presented including theoretical results. After that, the algorithm is applied on the disc process and numerical results for different choices of parameters are presented. The third chapter consists of two approaches for the estimation of parameters. First is the Takacs-Fiksel estimation procedure with a choice of weight functions as the derivatives of pseudolikelihood. The second one is the estimation procedure aiming for the optimal choice of weight functions for the estimation in order to provide better quality estimates. The theoretical background for both of these approaches is derived as well as detailed calculations for the disc process. The numerical results for both methods are presented as well as their comparison. 1

Submitted by (ana.araujo@ufrpe.br) on 2016-07-07T12:44:03Z No. of bitstreams: 1 Josimar Mendes de Vasconcelos.pdf: 4725831 bytes, checksum: 716f4b6bc6100003772271db252915b7 (MD5) / Made available in DSpace on 2016-07-07T12:44:03Z (GMT). No. of bitstreams: 1 Josimar Mendes de Vasconcelos.pdf: 4725831 bytes, checksum: 716f4b6bc6100003772271db252915b7 (MD5) Previous issue date: 2011-08-08 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The last years has increased the quantity of researchers and search scientific in the plantation, production and value of the soybeans in the Brazil, in grain. In front of this, the present dissertation looks for to analyze the data and estimate models that explain, of satisfactory form, the variability observed of the quantity produced and value of the production of soya in grain in the Brazil, in the field of the study. For the development of these analyses is used the classical and Bayesian inference, in the context of simultaneous equations by the tools of indirect square minimum in two practices. In the classical inference uses the estimator of square minima in two practices. In the Bayesian inference worked the method of Mountain Carlo via Chain of Markov with the algorithms of Gibbs and Metropolis-Hastings by means of the technician of simultaneous equations. In the study, consider the variable area harvested, quantity produced, value of the production and gross inner product, in which it adjusted the model with the variable answer quantity produced and afterwards the another variable answer value of the production for finally do the corrections and obtain the final result, in the classical and Bayesian method. Through of the detours normalized, statistics of the proof-t, criteria of information Akaike and Schwarz normalized stands out the good application of the method of Mountain Carlo via Chain of Markov by the algorithm of Gibbs, also is an efficient method in the modelado and of easy implementation in the statistical softwares R & WinBUGS, as they already exist smart libraries to compile the method. Therefore, it suggests work the method of Mountain Carlo via chain of Markov through the method of Gibbs to estimate the production of soya in grain. / Nos últimos anos tem aumentado a quantidade de pesquisadores e pesquisas científicas na plantação, produção e valor de soja no Brasil, em grão. Diante disso, a presente dissertação busca analisar os dados e ajustar modelos que expliquem, de forma satisfatória, a variabilidade observada da quantidade produzida e valor da produção de soja em grão no Brasil, no campo do estudo. Para o desenvolvimento dessas análises é utilizada a inferência clássica e bayesiana, no contexto de equações simultâneas através da ferramenta de mínimos quadrados em dois estágios. Na inferência clássica utiliza-se o estimador de mínimos quadrados em dois estágios. Na inferência bayesiana trabalhou-se o método de Monte Carlo via Cadeia de Markov com os algoritmos de Gibbs e Metropolis-Hastings por meio da técnica de equações simultâneas. No estudo, consideram-se as variáveis área colhida, quantidade produzida, valor da produção e produto interno bruto, no qual ajustou-se o modelo com a variável resposta quantidade produzida e depois a variável resposta valor da produção para finalmente fazer as correções e obter o resultado final, no método clássico e bayesiano. Através, dos desvios padrão, estatística do teste-t, critérios de informação Akaike e Schwarz normalizados destaca-se a boa aplicação do método de Monte Carlo via Cadeia de Markov pelo algoritmo de Gibbs, também é um método eficiente na modelagem e de fácil implementação nos softwares estatísticos R & WinBUGS, pois já existem bibliotecas prontas para compilar o método. Portanto, sugere-se trabalhar o método de Monte Carlo via cadeia de Markov através do método de Gibbs para estimar a produção de soja em grão, no Brasil.

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

[pt] Esta tese propõe uma metodologia de estimativa de pressão de poros em rochasreservatório através dos atributos sísmicos velocidade compressional V(p) e velocidade cisalhante V(s). Na metodologia, os atributos são encarados como observações realizadas sobre um sistema físico, cujo comportamento depende de um determinado número de grandezas não observáveis, dentre as quais a pressão de poros é apenas uma delas. Para estimar a pressão de poros, adota-se uma abordagem Bayesiana de inversão. Através de uma função de verossimilhança, estabelecida através de um modelo de física de rochas calibrável para a região, e do teorema de Bayes, combina- se as informações pré-existentes sobre os parâmetros de rocha, fluido e estado de tensões com os atributos sísmicos observados, inferindo probabilisticamente a pressão de poros. Devido a não linearidade do problema e ao interesse de se realizar uma rigorosa análise de incertezas, um algoritmo baseado em simulações de Monte Carlo (um caso especial do algoritmo de Metropolis- Hastings) é utilizado para realizar a inversão. Exemplos de aplicação da metodologia proposta são simulados em reservatórios criados sinteticamente. Através dos exemplos, demonstra-se que o sucesso da previsão de pressão de poros depende da combinação de diferentes fatores, como o grau de conhecimento prévio sobre os parâmetros de rocha e fluido, a sensibilidade da rocha perante a variação de pressões diferenciais e a qualidade dos atributos sísmicos. Visto que os métodos existentes para previsão de pressão de poros utilizam somente o atributo V(p) , a contribuição do atributo V(s) na previsão é avaliada. Em um cenário de rochas pouco consolidadas (ou em areias), demonstra-se que o atributo V(s) pode contribuir significativamente na previsão, mesmo apresentando grandes incertezas associadas. Já para um cenário de rochas consolidadas, demonstra-se que as incertezas associadas às pressões previstas são maiores, e que a contribuição do atributo V(s) na previsão não é tão significativa quanto nos casos de rochas pouco consolidadas. / [en] This work proposes a method for pore pressure prediction in reservoir rocks through compressional- and shear-velocity data (seismic attributes). In the method, the attributes are considered observations of a physic system, which behavior depends on a several not-observable parameters, where the pore pressure is only one of these parameters. To estimate the pore pressure, a Bayesian inversion approach is adopted. Through the use of a likelihood function, settled through a calibrated rock physics model, and through the Bayes theorem, the a priori information about the not-observable parameters (fluid and rock parameters and stress state) is combined with the seismic attributes, inferring probabilistically the pore pressure. Due the non-linearity of the problem, and due the uncertainties analysis demanding, an algorithm based on Monte Carlo simulations (a special case of the Metropolis- Hastings algorithm) is used to solve the inverse problem. The application of the proposed method is simulated through some synthetic examples. It is shown that a successfully pore pressure prediction in reservoir rocks depends on a set of factors, as how sensitive are the rock velocities to pore pressure changes, the a priori information about rock and fluid parameters and the uncertainties associates to the seismic attributes. Since the current methods for pore pressure prediction use exclusively the attribute compressional velocity V(p), the contribution of the attribute shear velocity V(s) on prediction is evaluated. In a poorly consolidated rock scenario (or in sands), the V(s) data, even with great uncertainties associated, can significantly contribute to a better pore pressure prediction. In a consolidated rock scenario, the uncertainties associated to pore pressure estimates are higher, and the s V data does not contribute to pore pressure prediction as it contributes in a poorly consolidated rock scenario.

Nous présentons dans ce mémoire un nouvel algorithme de type Metropolis-Hastings dans lequel la distribution instrumentale a été conçue pour l'estimation de distributions cibles bimodales. En fait, cet algorithme peut être vu comme une modification de l'algorithme Metropolis de type marche aléatoire habituel auquel on ajoute quelques incréments de grande envergure à des moments aléatoires à travers la simulation. Le but de ces grands incréments est de quitter le mode de la distribution cible où l'on se trouve et de trouver l'autre mode. Par la suite, nous présentons puis démontrons un résultat de convergence faible qui nous assure que, lorsque la dimension de la distribution cible croît vers l'infini, la chaîne de Markov engendrée par l'algorithme converge vers un certain processus stochastique qui est continu presque partout. L'idée est similaire à ce qui a été fait par Roberts et al. (1997), mais la technique utilisée pour la démonstration des résultats est basée sur ce qui a été fait par Bédard (2006). Nous proposons enfin une stratégie pour trouver la paramétrisation optimale de notre nouvel algorithme afin de maximiser la vitesse d'exploration locale des modes d'une distribution cible donnée tout en estimant bien la pondération relative de chaque mode. Tel que dans l'approche traditionnellement utilisée pour ce genre d'analyse, notre stratégie passe par l'optimisation de la vitesse d'exploration du processus limite. Finalement, nous présentons des exemples numériques d'implémentation de l'algorithme sur certaines distributions cibles, dont une ne respecte pas les conditions du résultat théorique présenté. / In this thesis, we present a new Metropolis-Hastings algorithm whose proposal distribution has been designed to successfully estimate bimodal target distributions. This sampler may be seen as a variant of the usual random walk Metropolis sampler in which we propose large candidate steps at random times. The goal of these large candidate steps is to leave the actual mode of the target distribution in order to find the second one. We then state and prove a weak convergence result stipulating that if we let the dimension of the target distribution increase to infinity, the Markov chain yielded by the algorithm converges to a certain stochastic process that is almost everywhere continuous. The theoretical result is in the flavour of Roberts et al. (1997), while the method of proof is similar to that found in Bédard (2006). We propose a strategy for optimally parameterizing our new sampler. This strategy aims at optimizing local exploration of the target modes, while correctly estimating the relative weight of each mode. As is traditionally done in the statistical literature, our approach consists of optimizing the limiting process rather than the finite-dimensional Markov chain. Finally, we illustrate our method via numerical examples on some target distributions, one of which violates the regularity conditions of the theoretical result.

In this thesis, a new approach for generating reaction time predictions for Bayesian cognitive models of sequential decision-making is proposed. The method is based on a Markov chain Monte Carlo algorithm that, by utilizing prior distributions and likelihood functions of possible action sequences, generates predictions about the time needed to choose one of these sequences. The plausibility of the reaction time predictions produced by this algorithm was investigated for simple exemplary distributions as well as for prior distributions and likelihood functions of a Bayesian model of habit learning. Simulations showed that the reaction time distributions generated by the Markov chain Monte Carlo sampler exhibit key characteristics of reaction time distributions typically observed in decision-making tasks. The introduced method can be easily applied to various Bayesian models for decision-making tasks with any number of choice alternatives. It thus provides the means to derive reaction time predictions for models where this has not been possible before. / In dieser Arbeit wird ein neuer Ansatz zum Generieren von Reaktionszeitvorhersagen für bayesianische Modelle sequenzieller Entscheidungsprozesse vorgestellt. Der Ansatz basiert auf einem Markov-Chain-Monte-Carlo-Algorithmus, der anhand von gegebenen A-priori-Verteilungen und Likelihood-Funktionen von möglichen Handlungssequenzen Vorhersagen über die Dauer einer Entscheidung für eine dieser Handlungssequenzen erstellt. Die Plausibilität der mit diesem Algorithmus generierten Reaktionszeitvorhersagen wurde für einfache Beispielverteilungen sowie für A-priori-Verteilungen und Likelihood-Funktionen eines bayesianischen Modells zur Beschreibung von Gewohnheitslernen untersucht. Simulationen zeigten, dass die vom Markov-Chain-Monte-Carlo-Sampler erzeugten Reaktionszeitverteilungen charakteristische Eigenschaften von typischen Reaktionszeitverteilungen im Kontext sequenzieller Entscheidungsprozesse aufweisen. Das Verfahren lässt sich problemlos auf verschiedene bayesianische Modelle für Entscheidungsparadigmen mit beliebig vielen Handlungsalternativen anwenden und eröffnet damit die Möglichkeit, Reaktionszeitvorhersagen für Modelle abzuleiten, für die dies bislang nicht möglich war.

L'action publique locale dans les métropoles. Le cas de la gestion du commerce de rue à Mexico et Lima. Alors que la gouvernance métropolitaine fait l'objet de nombreux travaux en sciences sociales, les gouvernements locaux infra-métropolitains sont moins étudiés. Or, ils continuent d'être les acteurs principaux de la régulation des espaces urbains. Ils agissent de manière autonome sur leur territoire tout en étant dans une situation d'inter-territorialité spécifique au milieu urbain. L'analyse comparative de la gestion du commerce de rue à Mexico et Lima montre la mise en œuvre de l'action publique dans les territoires administratifs des métropoles. Elle distingue les centres historiques - vitrines et laboratoires des autorités régionales - des territoires municipaux où les politiques oscillent entre imitation, innovation et inertie. De plus, elle révèle une palette de processus et interactions horizontales et verticales entre les actions publiques des différentes autorités, alimentant le débat sur la fragmentation urbaine / Local public action in the metropolis. Case study of street vending policies in Mexico City and Lima. While metropolitan governance is the subject of much research in social sciences, local and infra-metropolitan governments have been studied less. However, they are still the main actors of urban space regulation. They act autonomously in their territories and are simultaneously in a situation of inter-territoriality specific to the urban environment. The comparative analysis of street vending policies in Mexico City and Lima displays the implementation of local public action in the administrative territories of the metropolis. It distinguishes historical centres –the showcases and laboratories of regional authorities– from municipal territories where the policies fluctuate between imitation, innovation and inertia. Likewise, the analysis contributes to the debate on urban fragmentation by revealing a range of horizontal and vertical interactions and processes between the public actions of the different authorities